
"""simple docstring"""



import sys
def    _UpperCAmelCase (					__lowerCamelCase  :			int						)	->   int:
  _snake_case   	=			len(lowerCamelCase_						)
  _snake_case   	=			[[0 for x in range(lowerCamelCase_						)] for x in range(lowerCamelCase_						)]
  _snake_case   	=			[[0 for x in range(lowerCamelCase_						)] for x in range(lowerCamelCase_						)]

  for chain_length in range(2					,   lowerCamelCase_						):
    for a in range(1					,   n - chain_length + 1						):
      _snake_case   	=			a + chain_length - 1

      _snake_case   	=			sys.maxsize
      for c in range(lowerCamelCase_					,   lowerCamelCase_						):
        _snake_case   	=			(
            matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
        )
        if cost < matrix[a][b]:
          _snake_case   	=			cost
          _snake_case   	=			c
  return matrix, sol
def    _UpperCAmelCase (					__lowerCamelCase  :			List[str]					,   __lowerCamelCase  :			List[str]					,   __lowerCamelCase  :			Any						)	->   Tuple:
  if i == j:
    print('''A''' + str(lowerCamelCase_						)					,   end=''' '''						)
  else:
    print('''('''					,   end=''' '''						)
    print_optiomal_solution(lowerCamelCase_					,   lowerCamelCase_					,   optimal_solution[i][j]						)
    print_optiomal_solution(lowerCamelCase_					,   optimal_solution[i][j] + 1					,   lowerCamelCase_						)
    print(''')'''					,   end=''' '''						)
def    _UpperCAmelCase (					)	->   Optional[int]:
  _snake_case   	=			[30, 35, 15, 5, 10, 20, 25]
  _snake_case   	=			len(lowerCamelCase_						)
  # Size of matrix created from above array will be
  # 30*35 35*15 15*5 5*10 10*20 20*25
  _snake_case   	=			matrix_chain_order(lowerCamelCase_						)

  print('''No. of Operation required: ''' + str(matrix[1][n - 1]						)						)
  print_optiomal_solution(lowerCamelCase_					,   1					,   n - 1						)


if __name__ == "__main__":
 main()






from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_ = "x"     ,				lowerCamelCase_ = 10**-10     ,				lowerCamelCase_ = 1     ,				):
							A      :					int      		=					symbols(lowerCamelCase_		)
							A      :					List[str]      		=					lambdify(lowerCamelCase_     ,				lowerCamelCase_		)
							A      :					Tuple      		=					lambdify(lowerCamelCase_     ,				diff(lowerCamelCase_     ,				lowerCamelCase_		)		)

							A      :					Optional[int]      		=					starting_point

							while True:
														if diff_function(lowerCamelCase_		) != 0:
																					A      :					Union[str, Any]      		=					prev_guess - multiplicity * func(lowerCamelCase_		) / diff_function(
																					    lowerCamelCase_		)
														else:
																					raise ZeroDivisionError('''Could not find root'''		) from None

														# Precision is checked by comparing the difference of consecutive guesses
														if abs(next_guess - prev_guess		) < precision:
																					return next_guess

														A      :					Tuple      		=					next_guess


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(F"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

		# Find root of polynomial
		# Find fourth Root of 5
		print(F"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}")

		# Find value of e
		print(
		    "The root of log(y) - 1 = 0 is ",
		    F"{newton_raphson('log(y) - 1', 2, variable='y')}",
		)

		# Exponential Roots
		print(
		    "The root of exp(x) - 1 = 0 is",
		    F"{newton_raphson('exp(x) - 1', 10, precision=0.0_05)}",
		)

		# Find root of cos(x)
		print(F"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")






